Subject: [mg131990] Re: unser-interface problems using Mathematica as a calculator

From: Daniel <dosadchy at its.jnj.com>

Date: Tue, 12 Nov 2013 00:15:10 -0500 (EST)

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> The example below illustrates why Mathematica's
> display rules for approximate numbers are very
> confusing for students. Should this be considered a
> user-interface bug? If not, why not? In any case, can
> the default display be changed to something more
> familiar from spreadsheets and other computing
> languages?
> Thanks,
> Alan Isaac
>
> In[217]:= tv = TimeValue[1, 0.04, 3]
> tv == 1.124864
> tv == 1.12486
>
> Out[217]= 1.12486
>
> Out[218]= True
>
> Out[219]= False
>
A statement like this "x == 1.123" is usually a bug (except in a very very VERY specific circumstances), and students should not use it.
The the value of x is usually a result of an expression, and different, but mathematically identical implementations of the expression will usually give slightly different numerical results.
The test should be: "Abs[x - 1.123] < EPS", where EPS is a small number that depends on the estimation of numerical truncation errors (which depends on the expression).